/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date:        15. February 2012
* $Revision: 	V1.1.0
*
* Project: 	    CMSIS DSP Library
* Title:		arm_var_q15.c
*
* Description:	Variance of an array of Q15 type.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.1.0 2012/02/15
*    Updated with more optimizations, bug fixes and minor API changes.
*
* Version 1.0.10 2011/7/15
*    Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
*    Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
*    Documentation updated.
*
* Version 1.0.1 2010/10/05
*    Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
*    Production release and review comments incorporated.
* -------------------------------------------------------------------- */

#include "arm_math.h"

/**
 * @ingroup groupStats
 */

/**
 * @addtogroup variance
 * @{
 */

/**
 * @brief Variance of the elements of a Q15 vector.
 * @param[in]       *pSrc points to the input vector
 * @param[in]       blockSize length of the input vector
 * @param[out]      *pResult variance value returned here
 * @return none.
 *
 * @details
 * <b>Scaling and Overflow Behavior:</b>
 *
 * \par
 * The function is implemented using a 64-bit internal accumulator.
 * The input is represented in 1.15 format.
 * Intermediate multiplication yields a 2.30 format, and this
 * result is added without saturation to a 64-bit accumulator in 34.30 format.
 * With 33 guard bits in the accumulator, there is no risk of overflow, and the
 * full precision of the intermediate multiplication is preserved.
 * Finally, the 34.30 result is truncated to 34.15 format by discarding the lower
 * 15 bits, and then saturated to yield a result in 1.15 format.
 *
 */


void arm_var_q15(
    q15_t* pSrc,
    uint32_t blockSize,
    q31_t* pResult)
{
	q31_t sum = 0;                                 /* Accumulator */
	q31_t meanOfSquares, squareOfMean;             /* Mean of square and square of mean */
	q15_t mean;                                    /* mean */
	uint32_t blkCnt;                               /* loop counter */
	q15_t t;                                       /* Temporary variable */
	q63_t sumOfSquares = 0;                        /* Accumulator */

#ifndef ARM_MATH_CM0

	/* Run the below code for Cortex-M4 and Cortex-M3 */

	q31_t in;                                      /* Input variable */
	q15_t in1;                                     /* Temporary variable */

	/*loop Unrolling */
	blkCnt = blockSize >> 2u;

	/* First part of the processing with loop unrolling.  Compute 4 outputs at a time.
	 ** a second loop below computes the remaining 1 to 3 samples. */
	while(blkCnt > 0u) {
		/* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1])  */
		/* Compute Sum of squares of the input samples
		 * and then store the result in a temporary variable, sum. */
		in = *__SIMD32(pSrc)++;
		sum += ((in << 16) >> 16);
		sum += (in >> 16);
		sumOfSquares = __SMLALD(in, in, sumOfSquares);
		in = *__SIMD32(pSrc)++;
		sum += ((in << 16) >> 16);
		sum += (in >> 16);
		sumOfSquares = __SMLALD(in, in, sumOfSquares);

		/* Decrement the loop counter */
		blkCnt--;
	}

	/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
	 ** No loop unrolling is used. */
	blkCnt = blockSize % 0x4u;

	while(blkCnt > 0u) {
		/* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
		/* Compute Sum of squares of the input samples
		 * and then store the result in a temporary variable, sum. */
		in1 = *pSrc++;
		sum += in1;
		sumOfSquares = __SMLALD(in1, in1, sumOfSquares);

		/* Decrement the loop counter */
		blkCnt--;
	}

	/* Compute Mean of squares of the input samples
	 * and then store the result in a temporary variable, meanOfSquares. */
	t = (q15_t)((1.0f / (float32_t)(blockSize - 1u)) * 16384);
	sumOfSquares = __SSAT((sumOfSquares >> 15u), 16u);

	meanOfSquares = (q31_t)((sumOfSquares * t) >> 14u);

#else

	/* Run the below code for Cortex-M0 */

	q15_t in;                                      /* Temporary variable */
	/* Loop over blockSize number of values */
	blkCnt = blockSize;

	while(blkCnt > 0u) {
		/* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
		/* Compute Sum of squares of the input samples
		 * and then store the result in a temporary variable, sumOfSquares. */
		in = *pSrc++;
		sumOfSquares += (in * in);

		/* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
		/* Compute sum of all input values and then store the result in a temporary variable, sum. */
		sum += in;

		/* Decrement the loop counter */
		blkCnt--;
	}

	/* Compute Mean of squares of the input samples
	 * and then store the result in a temporary variable, meanOfSquares. */
	t = (q15_t)((1.0f / (float32_t)(blockSize - 1u)) * 16384);
	sumOfSquares = __SSAT((sumOfSquares >> 15u), 16u);
	meanOfSquares = (q31_t)((sumOfSquares * t) >> 14u);

#endif /* #ifndef ARM_MATH_CM0 */

	/* Compute mean of all input values */
	t = (q15_t)((1.0f / (float32_t)(blockSize * (blockSize - 1u))) * 32768);
	mean = __SSAT(sum, 16u);

	/* Compute square of mean */
	squareOfMean = ((q31_t) mean * mean) >> 15;
	squareOfMean = (q31_t)(((q63_t) squareOfMean * t) >> 15);

	/* Compute variance and then store the result to the destination */
	*pResult = (meanOfSquares - squareOfMean);

}

/**
 * @} end of variance group
 */
